8litres of a 10 % acid solution must be used
32litres of a 35 % acid solution must be used
Let the liters each of a 10 % acid solution be given as "x"
A 35 % acid solution = 40 - x
The weighted combination for x and 40-x is given as:
[tex]0.1x+0.35(40-x)=0.30(40)[/tex]Solve the expression for x:
[tex]\begin{gathered} 0.1x+0.35(40-x)=0.30(40) \\ 0.1x+14-0.35x=12 \\ -0.25x+14=12 \\ -0.25x=12-14 \\ -0.25x=-2 \\ x=\frac{2}{0.25} \\ x=8 \end{gathered}[/tex]This shows that 8litres of a 10 % acid solution must be used
For the 35% solution, the amount of litres used is:
40 - x = 40 - 8 = 32litres
Hence 32 liters of a 35 % acid solution must be used.
